After university, in 1979, Mellon went to work as a trainee fund manager at Griffin Thornton (GT Management), spending six months in Hong Kong, before moving to San Francisco. Leaving with Richard Thornton in 1984 to cofound Thornton Management, Mellon returned to Hong Kong to run the company's operation there. Thornton sold for £25 million four years later, making him a millionaire aged 28. He then spent two years setting-up a Hong Kong operation for Tyndall Holdings.[4][5][3]

Along with Jayne Sutcliffe in 1992, he founded Regent Pacific as an emerging markets investment vehicle, with Sir John Templeton their first customer. In 1994 came what Mellon calls his "first really big break". Having read about privatization in Russia he traveled to Vladivostok, and later Moscow, where he found Russians selling vouchers on the streets that could be swapped for stock in Russian industries. In a single day he and Sutcliffe spent $2 million in the covered markets buying the vouchers for about $25 each. A few weeks later the shares were worth $17 million.[3][4]

A spin-off of from Regent Pacific that specialises in Eastern Europe, the fund management firm Charlemagne Capital, was also founded in the 1990s and listed on the stock market in 2006.[3][6]

The 1998 Russian financial crisis was disastrous for Regent, with the value of investments in the company's Russian and East European funds becoming almost worthless, and most of its cash tied-up in local currency bonds as the rouble was devalued.[5]

When Regent Pacific acquired a stake in Hambros Bank, Mellon launched a public attack on the board's performance which preceded the break-up of the bank. This and Regent's methods of breaking-up of closed-end funds led to a 1997 Business Week article referring to him and the company's investment director, Peter Everington as "the Bad Boys of Emerging Markets". In 2009 Mellon said "in hindsight I was overly vociferous, and I have not done it again like that — I’m now more behind the scenes".[3][7]

Along with Stephen Dattels, Mellon founded the uranium mining company Uramin in 2005 with just $100,000. Also listed on the stock market in 2006, it sold the following year to Areva for around £1.6 billion, reportedly making him about £80 million. Areva later had to accept a huge write-down in Uramin's value.[4][8]

He is still non-executive chairman at Regent Pacific,[9] and the executive co-chairman of the board of Fast Forward Innovations (formerly Kuala Innovations),[10] the non-executive chairman at Speymill Deutsche Immobilien Company PLC, Port Erin Biopharma Investments Limited and SalvaRx Group PLC (formerly 3Legs Resources).[11] He also holds non-executive directorships at Condor Gold PLC, Bradda Head Limited (formerly Life Science Developments) and Portage Biotech Inc.[12] He is also chairman of the Burnbrae Group.[13][14] And also founder and co-chairman (along with Johnny Hon) of Mann Bioinvest.[15]

Mellon has said he (financially) “had a good day” after the Brexit vote with his trades returning almost 25 percent profit on the year.[22]

Juvenescence, a biotech company, was founded by Mellon and four others, Greg Bailey, Declan Doogan, Anthony Chow, and Alexander Pickett, in 2016. In 2018, Juvenescence raised $50 million, in a series A financing round.[23][24] Mellon has invested in longevity medicine company AgeX Therapeutics and other biotechnology companies, via Juvenescence and other investment vehicles.[25][26]

In 2009 Mellon was a leading financial backer of Prime Minister David Cameron and critical of the Labour government's "crazy crackdown on the non-domiciles who bring so much money and expertise into the country".[3]

He donated up to £100,000 towards campaigns to leave the EU in 2015.[29]

In March 2016, Mellon said he was less “ideologically committed” to Brexit than his friend Arron Banks, and that there were “good arguments to be made on both sides” of what he saw as a “nuanced” debate.[30]

In November 2016, Mellon felt that "Brexit is going to be a sideshow to the problems of Europe" and predicted that the Euro would not last, saying that "the euro as it stands at the moment is just a very inappropriate mechanism — I give the euro between one and five years of life."[22] He also serves on the executive board of the Initiative for Free Trade, a London-based research foundation founded by another prominent leave-supporter Daniel HannanMEP, after the Brexit vote, that aims to promote free trade.[31][32]

In July 2018, Mellon said there would be "a second referendum" that "remain will win".[33]